I don't follow. Clearly mammals aren't closely related to birds, dinosaurs, & "modern reptiles," but there are also a number of much older animals, in the Carboniferous & Permian eras, that are classified as reptiles.

For its ancestors to include both synapsida and diapsida, it would require interbreeding between wildly different species. Rather, it shares a common ancestor with both synapsida and diapsida.

However, it's true that it probably shouldn't be considered a reptile unless mammals are. Really, what we consider "reptiles" should probably be split into several different groups (testudines, squamates [possibly further split into squamates and sphenodonts], crocodilians, and dinosaurs [including birds]).

Paleothyris is at the base of a large clade, the Protosynapsida, defined as Paleothyris, Passer, their last common ancestor and all of its decendants. Casineria and the microsaurs are outgroups. The Protosynapsida includes the Synapsida and the Diapsida.

...must be incorrect. All I know is that I keep hearing that mammals evolved from reptiles in the Permian Era. Hence, the conclusion I keep coming to is that either all of those things are wrong, or mammals are descended from animals classed as reptiles.

I wish I had a scanner so I could show you exactly what I'm looking at, but I don't.

Mammals evolved from a common ancestor to reptiles, one which resembled modern reptiles more than modern mammals. Because of earlier scientific understanding, they were classified as reptiles, leading to a paraphyletic designation (that is, the descendants of a reptile should likewise be called reptiles). The common ancestor should be called something other than reptile under monophyletic definitions. I also think that reptilia should be split up. Right now, reptiles basically consist of everything in amniota left over after mammals and birds are taken out. The wastebin of amniotes.